I tend to think of Cave Story's world as a "sort of alternate fantasy reality" of ours, but most specifically a "console JRPG" world.
Like, think Chrono Trigger. The events of the game depict a historical timeline roughly similar to our own (barring things like the fact that we know humans and dinosaurs didn't exist at the same time in prehistory, though many, MANY works of fiction ignore this because dinosaurs are awesome) with a logical prehistory, medieval age, etc. The "main event" of the game occurs in 1999 A.D., which I believe was specifically chosen due to its apocolyptic nature as a date (the 2012 of a half-generation ago) and though technology is a bit more advanced than our own (people living in domes, androids on the precipice of being able to experience emotion) you still get this feeling like "the apocolypse is going to happen to this world not too unlike our own, and it's going to happen in what the player would consider to some degree the present day".
Obviously, in the end, Chrono Trigger's world is in no way our own, or even supposed to be, but it tries to feel "familiar" to the player, enough that he/she feels they're actually saving the world in some 16 bit video game sort of way.
There's also the fact that the entire world is absolutely tiny, with an average of one city per CONTINENT and a total of like three or four different cities in the world depending on era. And there are a million games like this. Even the largest JRPG worlds are usually like a pocket-sized "version" of our Earth.
I think that's what Cave Story's world is like. Pixel crafted a game and a world of his own that pays heavy homage to older console games of all types, not the least of which would be games in the RPG genre, even though CS itself hardly plays like one. If CS's world were our own Earth, every Mimiga in existence being turned rabid plus all of the power imaginably granted from the Demon Crown would hardly be enough to do anything more threatening than like a terrorist attack towards one single city of Date's choosing. However, if you consider an old RPG-sized world, and that island being as big as an empire in itself, it's logical. I keep thinking of an evil, more massive version of "Township" from Breath of Fire II floating around dumping frenzied mimigas and demons down on all the little towns (or "countries"), thus achieving complete dominance.
Cue RPG starring a random human whose absolute purpose in life is to travel the world, level up, get amazing equipment, find lovable party members, and finally ascend to the floating island and put a stop to Date and eventually Ballos himself. Of course, the world may well be in ruin by this point, but look at the ending of Final Fantasy 6 or 10 for example. Too bad the thought of CS officially ending with the bad ending would be really depressing!